Class 12 Physics Chapter 3: Current Electricity | Notes & Derivations

📅 Tuesday, 20 January 2026 📖 3-5 min read
Class 12 Physics • NCERT

Chapter 3: Current Electricity

Complete Textbook Edition (Ohm's Law, Kirchhoff & Cells)

Vol 1: Electric Current & Ohm's Law

Electric Current ($I$): The rate of flow of electric charge. $I = q/t$.
Unit: Ampere (A). Scalar Quantity.

Drift Velocity ($v_d$)

The average velocity with which free electrons get drifted towards the positive end of the conductor under the influence of an external electric field.

$$v_d = \frac{eE}{m}\tau$$

($\tau$ = Relaxation Time)

Relation between Current and Drift Velocity:

$$I = n e A v_d$$

Ohm's Law

At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.

$$V = IR$$

Vol 2: Resistivity & Temperature Dependence

Resistance ($R$): Opposition to current flow. $R = \rho \frac{l}{A}$.
Resistivity ($\rho$): Intrinsic property of material. Independent of dimensions.

Vector Form of Ohm's Law:
$$\vec{J} = \sigma \vec{E}$$
(Where $J$ = Current Density, $\sigma$ = Conductivity = $1/\rho$)

Temperature Dependence

Resistance increases with temperature for conductors.

$$R_t = R_0 (1 + \alpha \Delta T)$$
($\alpha$ = Temperature Coefficient of Resistance)

Vol 3: Cells & Kirchhoff's Rules

EMF ($\varepsilon$): Potential difference when circuit is open.
Terminal Voltage ($V$): Potential difference when circuit is closed.
Relation: $V = \varepsilon - Ir$ (During discharge).

Kirchhoff's Rules (KCL & KVL)

1. Junction Rule (KCL):
$\sum I_{in} = \sum I_{out}$
(Conservation of Charge)
2. Loop Rule (KVL):
$\sum \Delta V = 0$ in a closed loop.
(Conservation of Energy)

Vol 4: Wheatstone Bridge

An arrangement of 4 resistors used to determine unknown resistance.

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Balanced Condition:
When no current flows through Galvanometer ($I_g = 0$):

$$\frac{R_1}{R_2} = \frac{R_3}{R_4}$$

Note: The Slide Wire Bridge (Meter Bridge) works on this principle.

Vol 5: Mission 100 Question Bank

Section A: MCQs

Q1. Kirchhoff's Loop Rule is a consequence of conservation of:
(a) Charge   (b) Momentum   (c) Energy   (d) Mass
Ans: (c) Energy.

Q2. If the temperature of a conductor increases, its drift velocity:
(a) Increases   (b) Decreases   (c) Remains same
Ans: (b) Decreases (Relaxation time $\tau$ decreases due to more collisions).

Section B: Numericals (Important)

Q3. A battery of EMF 10 V and internal resistance $3 \Omega$ is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage?

Solution:
Given: $\varepsilon = 10$ V, $r = 3 \Omega$, $I = 0.5$ A.
1. $\varepsilon = I(R+r) \Rightarrow 10 = 0.5(R + 3)$
$20 = R + 3 \Rightarrow R = 17 \Omega$.
2. $V = \varepsilon - Ir = 10 - (0.5 \times 3) = 10 - 1.5 = 8.5$ V.
Ans: $17 \Omega$, 8.5 V.

Section C: Conceptual

Q4. Why is a potentiometer preferred over a voltmeter for measuring EMF?
Ans: A potentiometer works on the null deflection method (draws no current from the cell at balance point), so it measures the true EMF. A voltmeter always draws some current, measuring terminal voltage ($V < \varepsilon$).

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